I wonder how bitcoin would handle it growth?I spent ~6 hours downloading all blocks. It also took almost 200Mb on disk. I wonder what would happen if bitcoins would be used 100 times more than now. Will it take 600 hours to download blocks for new clients and will it use 20Gb then?

Current implementations of the bitcoin client download the entire block chain, but future versions will not have to. There is a technique called Merkle tree (http://en.wikipedia.org/wiki/Hash_tree) that is used in the system which allows you to delete old and not-relevant-to-you transactions. It has the potential to scale extremely well.